31 If f(x, y) = e³¹ sin 9y, then fry is given by:

Q: 54 (b) y =. sin 2x. 4 Find

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Q: Given f(x,y,z) = sin (2xy) + 4xyz³. Find fzzx(3,3,3). Answer:

A: Solving the problem by doing partial derivative.

Q: tan(v) In(cos(v))dv.

A: Assume lncosv = t Differentiate both sides

Q: 3. Compute : exp (sin (e).

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Q: Evaluate y sin(xy) dA, where R = [1, 2] × [0, π]. R

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Q: 3. If G = (2x²y – x*)î + (e*y + y sin x)j+ (x² cos y)k, find: %3D дхду

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Q: 3. Let w = f(z) = 5z² – 12z + 3 + 2i a. Determine u and v b. Calculate f (3 – 4i)

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Q: Given f(x,y,z) = sin (5xy) + 3xyz3. Find fzzx(5,2,3). %3D zZx Answer:

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Q: I. Evaluate the following: a. (x³ + cos y + 5 dy = - 3yx²) dx b. xdy – ydx = (4x2 + y2)dy c. dx +…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Consider the functions f(r) = In(x/8), g(x) = h(z) = e* +8, p{x)=e" q(x) 18 r(x) = 8e and s(#) !3!…

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Q: Evaluate r(2) and r(-1) for r(t) = (sin 1,12, (1² + 1)~1). %3D

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Q: 3. V4- (x – 3)²dx.

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Q: dy 1.J ey sin( e-y )

A: Solved below

Q: Show that if Y = ax+ b (a ≠ O),then Corr(X, Y) =+1or -1. Under what conditions will p =+1?

A: Assume that X has has nonzero variance, since otherwise the correlation coefficient would be 0,…